CHEMMAT 121

Stress Formula

Force over cross sectional area perpendicular to F

Stress unit

Pascal (Pa)

Strain formula and conventional name

Stretch (epsilon) = Change in length over original length (L/Lo)

Strength definition

Amount of force a material can resist before failure

Tensometer results

Tensile strength of a material - Stress strain curve

1st key point on a stress strain curve

Yeild point - Marks the end of the elastic region where strain is recoverable

2nd key point on stress strain curve

Ultimate tensile stress (UTS). End of plastic deformation and start of necking

3rd point on stress strain curve

Fracture point (failure)

Plastic deformation - Concequence

Workhardening

Necking definition

Localised reduction in area

Plastic deformation definition

Uniform reduction in area

Elastic deformation definition

All strain is recovered when stress is removed

Fracture definition

1 Piece becomes multiple

Young’s modulus

Stiffness/Elasticity (E) = change in stress over change in strain. Unit of Pascals (Pa)

Strain unit

No unit, expressed as a percentage which is a ratio of change in the length over the original length

Fully annealed steel curve

Poisson’s ratio - Units

Nu (v)

Poisson’s ratio - equation

v = — x strain over z strain

0.2% Proof stress

Non-obvious yeild point

Safety factor assumptions

1) material is weaker than it actually is

2) applied force is larger than it actually is

Point at which materials are planned to resist up until

Yield point

True stress curve formula

True stress = Force over instantaneous area

Engineering stress curve formula

Same as standard stress calculation

Ductility definition

How much plastic deformation before fracture. Shown by strain axis

Brittle definition

No plastic deformation (or very little)

Elongation formula

Percentage of elongation = change in length over original length x 100 (same as strain)

Reduction in area formula

Percentage of reduction in area = change in area over original area x 100

Toughness definition

Energy required to fracture material

Toughness visual representation on curve

Area under the curve

Strength is mutually exclusive to

Toughness

Typical stress strain curves for different materials

Crystalline definition

Solid structures where the atoms arrange themselves in a regular repeating pattern

BCC

Body centered cubic

FCC

Face centered cubic

HCP

Hexagonal close-packed

BCC Model

Atoms per BCC cell

2

Coordination number definition

Number of nearest neighbour atoms for the BCC cell

BCC Coordination number

8

Unit cell dimension symbol

a

Unit cell dimension formula BCC

a = 4R over root(3)

R - term

Radius of atom

Atomic packing formula

Volume of atoms over volume of unit cell

BCC Atomic packing percentage (estimated)

68%

FCC Model

Atoms per FCC unit cell

4

FCC Coordination number

12

FCC Unit cell dimension formula

a = 4R over root(2)

FCC Atomic packing factor

74%

Hexagonal close packed model

Atoms per HCP cell

6

HCP Coordination number

12

HCP Atomic packing factor

74%

Polymorphism

Description for materials that can exist in more than 1 crystal structure.

Ceramic definition

Metal and non metal atoms joined together by ionic and covalent bonds arranged in a crystalline structure

Ceramic characteristics

Strong but brittle

2 Ceramic crystal structures

1) Rock salt structure

2) Silicate structure

Factors in determining ceramic crystal structures

1) Balancing charges to make final solid electrically neutral

2) Reliative size of ions (Anions and cations not touching)

Rock Salt structure model

Rock salt coordination number

6

Rock salt unit cell dimension formula

a = 2 x (Anion radius + cation radius)

Silicate structure model - Not unit cell

Hard sphere model:

Glass structure classification

Amorphus

Silicate structure factor

Cooling rate from liquid state

1) Slow cooling - Crystalline ceramic → atoms can rearrange

2) Rapid cooling - Amorphous glass → Can’t rearrange

Crystallography definition

The study of the geometric crystal structures in crystalline solids. Refers to planes and directions within the structure

Crystal lattice directions

[u v w]

Steps to name directions in a crystal lattice

1) Draw the direction vector from a chosen origin.

2) Project the length onto all 3 unit cell axes. ie. [1u, 0v, 1/2c]

3) Put in terms of coefficients ie. [1 0 1/2]

4) Convert to whole integers ie. [2 0 1]

5) Put in square brackets.

Negative direction notation

Bar above a number.

Crystallographically equivalent definition (directions)

Atomic spacing along one direction is the same as another

ie. [0 1 0]

Direction family notation

< ‘1 0 0’ >

Planes in a crystal lattice (notation & name)

Round brackets: ( h k l )

Called millerindicies

Steps to name planes in a crystal lattice

1) Decide origin point - CANNOT be on plane being named & plane should act like a ‘roof’ to the point.

2) Work out intercepts of plane on unit cell (from origin)

→ A flat or vertical plane will only have 1 intercept ie. [ 2 ∞ ∞ ] (100)

→ A diagonal plane (ie. up and across in 1 direction) will have 2 intercepts ie. [ 2 1 ∞ ] (110)

→ A Diagonal plane in all directions will have 3 intercepts

ie. [ 2 1 1/2] (111)

3) Take reciprocals of intercepts ie. [ 1 ½ ∞ ] → [ 1 2 0 ]

4) Convert to integers (if needed)

5) Put in round brackets

Close packed directions definition

Directions where atoms are touching

( 1 0 0 ) Atomic arrangements

( 1 1 0 ) Atomic arrangements

( 1 1 1 ) Atomic arrangements

Crystallographically equivalent definition (planes)

Atomic spacing on two different planes are the same.

ie. ( 1 0 0 ) has same spacing as ( 0 1 0 ) for FCC and BCC cells

Plane family notation

{ 1 0 0 }

Close-packed family of planes (FCC)

{ 1 1 1 } in < 1 1 0 > directions

→ Direction refers to a plane which is perpendicular to direction the vector [ 1 1 0 ]

Close packed family of planes (BCC)

None.

One family is closer-packed than others: { 1 1 0 } in < 1 1 1 > directions

More accurate stress/deformation definition

Atomic bonds stretching

Stress formula in terms of elasticity and strain

Stress = elasticity (E) x strain (epsilon)

Permanent deformation definiton

Atomic bonds break and reform

Deformation process term

SLIP

Close packed plane slip properties

1) Atoms don’t move far to next equilibrium position

2) Weaker material

Non close packed plane slip properties

1) Atoms have to move further to next equilibrium position

2) Stronger material

Theoretical strength definition

The energy required to break and remake atomic bonds.

Shear strength definition

Actual strength of a material due to imperfections

Examples of point defects (1D imperfections)

1) Interstitial atom

2) Substitutional atom

3) Vacancy

Examples of planar defects (2D imperfections)

1) Edge dislocation

2) Screw dislocation

Slip cause

Yield strength is exceeded. Occurs easier in arrangements with dislocation.

Slip definition

Dislocation movement

Arrangements with highest likelihood of slip

Close packed planes in close packed directions

Slip comparison between FCC and BCC

1) BCC are generally stronger and less ductile than FCC

2) Slip occurs easier in FCC structures

HCP Slip & Characteristics

1) Close packed planes lined up in 1 orientation

2) Slip is very difficult

3) Thus HCP structures are strong and brittle

Plastic deformation in ceramics

Improbable. Like charges (ie, cation & cation) don’t form bonds

Ceramics characteristics

1) Stiff - Strong ionic/covalent bonds

2) Brittle - Like charges moved together repel, causing fracture

Ceramic imperfections (1)

Porosity

Glass characteristics

1) Strong

2) Brittle

Polycrystalline definition

Solidifying molten metals form many crystals.